Question

Evaluate the numerical expression.



1/2 − (− 3/4)



Responses
A


1/3
B


1/4
C


3/2
D


5/4
E


7 4

Answer 1

Evaluate 4 1/2 - 2 - 5 2/3.


Responses
A
–3 1/6
B
12 1/1
C
2 1/6
D
–4 1/6

Answer 2

Determine the value of the expression –5.45 + 4.12 –8.66.
Responses
A -9.99
B 18.23
C –0.91
D –2.99

Answer 3

To evaluate the expression \( \frac{1}{2} - (-\frac{3}{4}) \), we start by simplifying it.

Subtracting a negative number is the same as adding the positive value of that number:

\[
\frac{1}{2} - (-\frac{3}{4}) = \frac{1}{2} + \frac{3}{4}
\]

Next, we need a common denominator to add the fractions. The common denominator of 2 and 4 is 4. We will convert \(\frac{1}{2}\) to a fraction with a denominator of 4:

\[
\frac{1}{2} = \frac{2}{4}
\]

Now we can write the expression as:

\[
\frac{2}{4} + \frac{3}{4} = \frac{2 + 3}{4} = \frac{5}{4}
\]

Thus, the value of the expression \( \frac{1}{2} - (-\frac{3}{4}) \) is:

\[
\frac{5}{4}
\]

Looking at the responses provided, the correct answer is:

**D: \( \frac{5}{4} \)**

Answer 4

To evaluate the expression \( 4 \frac{1}{2} - 2 - 5 \frac{2}{3} \), we first convert the mixed numbers to improper fractions.

1. Convert \( 4 \frac{1}{2} \):
\[
4 \frac{1}{2} = 4 \times 2 + 1 = 8 + 1 = \frac{9}{2}
\]

2. Convert \( 5 \frac{2}{3} \):
\[
5 \frac{2}{3} = 5 \times 3 + 2 = 15 + 2 = \frac{17}{3}
\]

Now, rewrite the expression using these improper fractions:
\[
\frac{9}{2} - 2 - \frac{17}{3}
\]

Next, we convert \(2\) to a fraction with the denominator of 1:
\[
2 = \frac{2}{1}
\]

Now, let's find a common denominator for \( \frac{9}{2} \), \( \frac{2}{1} \), and \( \frac{17}{3} \). The least common multiple (LCM) of the denominators 2, 1, and 3 is 6.

Convert each fraction:
- Convert \( \frac{9}{2} \) to a common denominator of 6:
\[
\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}
\]

- Convert \( \frac{2}{1} \) to a common denominator of 6:
\[
\frac{2}{1} = \frac{2 \times 6}{1 \times 6} = \frac{12}{6}
\]

- Convert \( \frac{17}{3} \) to a common denominator of 6:
\[
\frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6}
\]

Now we can rewrite the expression:
\[
\frac{27}{6} - \frac{12}{6} - \frac{34}{6}
\]

Since all fractions have the same denominator, subtract them:
\[
\frac{27 - 12 - 34}{6} = \frac{27 - 12 = 15}{6} - \frac{34}{6} = \frac{15 - 34}{6} = \frac{-19}{6}
\]

Now convert \(\frac{-19}{6}\) to a mixed number:
- Divide \(19\) by \(6\):
- \(19 \div 6 = 3\) (whole number)
- Remainder: \(19 - (6 \times 3) = 19 - 18 = 1\)

So, \(\frac{-19}{6}\) is:
\[
-3 \frac{1}{6}
\]

Thus, the evaluation of \( 4 \frac{1}{2} - 2 - 5 \frac{2}{3} \) gives us:
\[
\text{Final Answer: } -3 \frac{1}{6}
\]

The correct response is:

**A: \(-3 \frac{1}{6}\)**

Answer 5

To evaluate the expression \(-5.45 + 4.12 - 8.66\), we can perform the operations step by step.

1. First, add \(-5.45\) and \(4.12\):
\[
-5.45 + 4.12 = -1.33
\]

2. Next, subtract \(8.66\) from \(-1.33\):
\[
-1.33 - 8.66 = -10.00
\]

Thus, the value of the expression \(-5.45 + 4.12 - 8.66 = -10.00\).

Since \(-10.00\) is not listed among the options, let's double-check the calculations for accuracy.

### Confirming Steps:
- Starting with:
\[
-5.45 + 4.12 = -1.33 \quad \text{(this part is correct)}
\]
- Now for the next part:
\[
-1.33 - 8.66
\]
To perform this subtraction:
- Convert \(-1.33\) to an equivalent fraction:
- \(-1.33 = -1.33 - 8.66\)
- Adding the negatives:
\[
-1.33 + -8.66 = -10.00
\]

Now, the calculation seems consistent, but given that \(-10.00\) is not among the responses, it's essential to confirm the listed answers again.

### Evaluating Each Response Option:
- A: \(-9.99\)
- B: \(18.23\)
- C: \(-0.91\)
- D: \(-2.99\)

The subtraction \(-1.33 - 8.66\) did indeed give \(-10.00\). Since the options presented are certainly incorrect, it signals that a possible miscommunication or misprint in the options may exist.

### Final Answer:
The computed value of the expression is:
\[
\text{Value of expression} = -10.00
\]

If strictly choosing among the provided options based solely on proximity, \( \text{A: } -9.99 \) would be the nearest value based on a typical rounding error context, but it is essential to highlight this does not represent the exact calculation.